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12 December, 20:21

A die with 6 sides is rolled and the number on top is observed. What is the probability of rolling a die once and observing a number less than 5?

1/6

2/3

5/6

4

+2
Answers (1)
  1. 12 December, 20:34
    0
    So P (a 6 in two rolls) = P (6 in first roll) + P (6 in second roll) - P (6 in both rolls)

    = 1/6+1/6-1/6*1/6

    = 11/36

    You could have also used:

    P (a 6 in two rolls) = P (6 in the first roll only) + P (6 in the second roll only) + P (6 in both rolls)

    = 1/6*5/6 + 5/6*1/6 + 1/6*1/6

    = 11/36

    The above approach is not easy to handle when the number of rolls are increased.

    for two rolls:

    for three rolls:

    and so on ... Inclusion-exclusion principle

    Fortunately there is a better approach in this case, which will be clear if you see the venn diagrams in the link above,

    P (a 6 in two rolls) = 1 - P (no 6 in two rolls)

    P (no 6 in two rolls) = P (no 6 in first roll) * P (no 6 in second roll)

    and P (no 6 in first roll) = P (no 6 in second roll) = 5/6

    from there you get:

    P (a 6 in two rolls) = 1 - (5/6) ^2

    similarly for six rolls it will be 1 - (5/6) ^6 so its 'c'
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